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The Cauchy problem for Kawahara equation in Sobolev spaces with low regularity

✍ Scribed by Wei Yan; Yongsheng Li

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
214 KB
Volume
33
Category
Article
ISSN
0170-4214

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✦ Synopsis

This paper is devoted to studying the initial-value problem of the Kawahara equation. By establishing some crucial bilinear estimates related to the Bourgain spaces X s,b (R 2 ) introduced by Bourgain and homogeneous Bourgain spaces, which is defined in this paper and using I-method as well as L 2 conservation law, we show that this fifth-order shallow water wave equation is globally well-posed for the initial data in the Sobolev spaces H s (R) with s>-63 58 .

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